Mixed Practice Problems

1. Simplify: \( 2^4 \cdot 2^{-2} \)
2. Simplify: \( (x^3 y^2)^2 \cdot x^{-1} \)
3. Evaluate: \( 10^0 \), \( 3^{-2} \)
4. Write an exponential model for a population that triples every 5 days.
5. Graph \( y = 3^x \) and \( y = 2 \cdot 3^x \) on the same axes.
6. Compound interest: $1,500 at 4% annually, find total after 8 years.
7. Population growth: 600 bacteria doubles every 3 hours. Find population after 9 hours.
8. Radioactive decay: half-life of 5 hours, starting with 40g, amount after 15 hours?
9. Solve: \( 4^{x-1} = 64 \)
10. Describe the long-term behavior of \( y = 5 \cdot 2^x \) as \( x \to \infty \).